Foresight Update 10

page 3

Molecular
Carpentry

by Ted Kaehler

On his sabbatical from Apple Computer, Ted Kaehler worked
with the Foresight Institute on molecular systems design and
modeling:

In the everyday world, we work with building materials that can
be cut to size. When you are building a structure out of wood,
you measure the raw material and cut it to the proper dimensions.
Designs in the everyday world commonly use fixed 90 degree
angles, but variable lengths. Nanomechanical designs operate
under a different set of rules: bond lengths are virtually fixed,
but angles can be varied substantially. Designing a
nanomechanical structure is thus different from designing with a
material that can be cut to any desired size.

During the summer of 1990, I worked with Eric Drexler to develop
a system for designing molecular "parts" with arbitrary
length or angle requirements. Here is a typical problem we
considered: a designer has a nanometer scale device that needs to
be supported and held firmly in place (the required rigidity
varies with the application). Suppose the surrounding matrix is a
diamond crystal lattice (Fig.
1). For convenience, the designer has chosen hexagonal carbon
rings to serve as a standard interface. Every piece, including
the diamond lattice, has a triangle of three bonds coming
straight out of a hexagonal carbon ring which serves as its
attachment point. The problem is this: what arrangement of atoms
will bridge from the diamond crystal to a mounting ring on the
device and hold it firmly? Within the diamond, there are only
four distinct bond directions available, and at a limited set of
points in space. If we extend the crystal right up to the
mounting ring, it is unlikely that any of the bonds will closely
match it in angle or location. Thus we need a new arrangement of
atoms which will form a strong and stiff bridge from the crystal
to the device.

.

Figure 1. A diamond surface with a
six-membered ring attached.
The upper three carbon atoms (dark gray) are
shown with missing
bonds where the bracket would be extended. The
lower carbon atoms
are shown likewise, where the diamond crystal
would be extended.
The free surfaces are terminated with hydrogen
atoms (white) save
for three embedded nitrogens (light gray)
included to avoid the
need for crowded hydrogens. The illustrated
structure was minimized
using the MM2 potential energy function (Chem3D
Plus implementation).

Three methods for designing the bridge come to mind. The first
is to build the bridge atom by atom and "search" for
the proper configuration. This is much like a computer program
for playing chess. Placing an additional atom on the end of the
structure is like making a move in chess. One wants it to be a
step toward the solution, but one can't tell if it is the right
step, except by trying it. Only after more atoms are added (more
chess moves are made), can we tell whether the bridge matches up
at the far end (whether these moves lead to a better chess
position). If not, one must take back those moves and try others.
In the absence of a good predictive theory, this kind of search
takes a tremendous amount of computation, just as chess playing
programs do. Without this, designing a new bridge from scratch
every time one has a specific need does not look like such a good
idea.

The second method is to design a "universal" structure
that has length and angle adjustments. This would be a flexible
structure with many two-position adjustment points. These might
be chains that could be shortened by one atom, or atoms with
different bond lengths that could be substituted. By changing
which adjustment points were set to "long" and which
were "short," the length of the whole structure could
be varied by small amounts. Such a structure might have some
disadvantages. It would have to be large in order to get
sufficient variability. It is unlikely that it could be made very
stiff without being so large as to dwarf the device it was meant
to hold. We have not been able to think of any good structures
that avoid these problems, and this area is still open for
innovation.

The third method is to design hundreds of short, strong molecular
brackets and then classify them by offset and angle. After each
arrangement of atoms is designed, a program computes its detailed
shape, and the results are stored in a dictionary. The designer
uses the dictionary to choose the proper bracket to support the
device in its proper place. To choose the right bridge from the
catalog, we first imagine the diamond crystal extended up past
the mounting ring we are trying to secure. For the "number
one" atom on the mounting ring, we find its location within
a unit-cell of diamond crystal. We also note the angle in 3-space
of a vector that expresses the orientation of the ring. We then
look up the position and angle in the dictionary to find the
closest match. We find an entry for a known bracket and the
(x,y,z) offsets to each of its three attachment points in the
diamond lattice. The dictionary tells the designer what bracket
to use and where in the diamond lattice it will attach. The
bracket is free standing, attaching to the diamond crystal with
just three bonds (Fig. 1). In the final design, the diamond only
comes as close to the device as the offset says to, and the
bracket spans the remaining distance.

To design a family of brackets, we begin with a stack of
six-membered carbon rings. Such stacks are found within the
structure of hexagonal diamond (lonsdaleite) and are a strong,
compact structure (Fig. 2).
Each ring has three covalent bonds to the ring below and three to
the ring above. This gives good stiffness. A barrel-like stack of
six-membered rings is straight, so we must introduce some
variation to make it bend. One way is to use seven-membered
rings. Each seven-membered ring has three attachments above and
three below. The seventh atom distorts the ring in some
direction. A second seven-membered ring on top of the first has
six different places where the seventh atom can interrupt the
ring. The many combinations of seventh atoms on different levels
give a range of combined twists, bends, and offsets from the
normal lattice. All extra carbon bonds that hang out of the
structure are capped with hydrogen.

Figure 2. A stack of four six-membered
carbon rings. 'D' indicates the three bonds to the
diamond substrate. The top ring attaches to the device
being supported. Hydrogen atoms attached to the two
middle rings are not shown. (The structure appears to be
curving slightly to the left. It should be completely
straight, and we are looking for the bug in our
software.)

Figure 3 shows a
typical two-layered bracket with a hexagonal mounting ring on
each end. Even a structure of just two layers can have quite a
bit of twist and offset. The structure is compact and stiff, with
three or more covalent bonds at each cross-section. Here are the
major ways that a normal stack of six-membered carbon rings can
be varied to make brackets for cataloging:

Add a seventh atom in one of six places on a given ring.

Add another layer to the structure. Try both six-membered
and seven-membered rings in the new layer.

Substitute silicon for any of the carbon atoms. Silicon
has longer bonds and distorts the structure.

Substitute nitrogen for carbon. Substitute oxygen or
sulfur for carbon at the seventh atom (it is only bonded
to two other atoms).

Use a C=C double bond instead of a single bond. This only
works at certain places in the structure, and is
strained.

A side view of the stack shows six-membered rings facing
outward. When there is a seventh atom in a layer, the
side view shows a seven-membered ring. When two
seven-membered layers have their extra atom above each
other, the side view shows an eight-membered ring. That
ring can be split in two by adding a fourth bond between
the layers. The side view now shows two five-membered
rings. The extra bond between the layers changes the
shape of the bracket.

Similarly, a six-membered ring facing outward can be
bridged in a direction along the axis by adding a carbon,
oxygen, sulfur, or silicon (along with any needed
hydrogen atoms).

The computer program to build the catalog proceeds as follows:
Enumerate all the possible brackets using the above rules,
starting with the shortest first. For each bracket, compute its
shape using a molecular mechanics program. The most important
aspect of its shape are the three bonds coming out of the
mounting ring on each end. With one end attached to a diamond
lattice, we compute the offset and angle of the ring on the other
end, and enter it into the catalog. Since computing the shape of
the bracket is the hard part, we save time by making catalog
entries for the mirror image of the bracket, the bracket upside
down, and the bracket attached to a vertical face of the diamond
crystal.

Figure 3. The same structure with a
seventh atom inserted in two of the rings. The top ring
is rotated, displaced sideways, and tilted. Thousands of
such variations will be be classified in a catalog
according the location of their top ring. The designer
selects the bracket that matches the location of the part
he wishes to support.

Not every structure we compute will become an entry in the
catalog. When many brackets reach the same place and angle, we
only want the shortest and stiffest one. The catalog will be made
to a certain spatial and angular resolution. If we try to find
one entry for every 0.154 Å (a tenth of a carbon-carbon bond
length), then number of position points in a unit will be around
1029. For each of these, we need a variety of angles. Since bonds
can bend much more easily than they can change length, an angular
accuracy of plus or minus 10 degrees may suffice. Accounting for
all the spherical symmetries, we need 66 different angle entries
per approximate position, derived from as few as 4250 bracket
designs. (A single bracket may be entered into the table in as
many as 16 different ways.) The shape of many more than 4250
brackets will have to be computed to get a sufficient variety of
angles and locations. It will be interesting to see how clumpy
the distributions of brackets is, and to see if there are any
regularities that will allow us to predict the shape of an
as-yet-uncomputed bracket.

It is possible that reaching the full diversity of the catalog
will require putting too many layers in the bracket. Such a
bracket would be too long and floppy to be of much use. If this
is true, all brackets with more than a certain number layers will
be designed with thick bases. Imagine the thick base as a short
bracket made from three parallel hexagonal tubes. It is short and
stiff. On top of this is a normal one-tube bracket. The richer
structure of the thicker bracket allow it to have many more
variations per layer, making a diverse set of shapes easier to
generate.

If the designer is not happy with the spatial and angular
resolution he finds in the catalog, he can pull a few tricks. The
device he is building is likely to be anchored at several places.
If one of those anchors is at a slightly wrong place, he can pick
the other anchors to push the structure back in the right
direction. Likewise, slightly wrong angles can be pitted against
each other to give a correct final position. Such a mildly
strained structure should work just fine.

To begin the project, we selected an existing molecular mechanics
program. Programs that compute the shapes of molecules come in a
variety of speeds. The structures we are simulating contain
nothing but the atoms and bonds of locally-unremarkable organic
molecules. We are not studying unstable transition states in
chemical reactions, so we don't need "molecular
orbital" programs that model the quantum mechanics of
electron clouds. Instead we used a "molecular
mechanics" program that treats each chemical bond as a
spring with a certain resting length. Additional springs handle
the desire of an atom to keep its bonds at certain angles to each
other. By using only forces between the centers of atoms, this
program can go very fast. The program we selected is STRFIT3 by
Martin Saunders and Ronald Jarret of Yale University, which gives
results closely approximating those of the classic MM2 program .
Around this we are building programs to generate the brackets and
enter them in the catalog after their shape is known.

This system is implemented in Digitalk Smalltalk/V Mac on an
accelerator-assisted Macintosh II. After we have verified that
STRFIT3 is producing shapes that agree with known molecules, we
intend to run the system every night and build a catalog of
nanomechanical brackets.

The interesting thing about this project is considering design
problems in a world in which angles can be varied but lengths
cannot, with lengths and flexible angles like those found in real
molecules. The catalog we build now will probably not be the one
used when nanostructures are actually built. By the time
fabrication technology is available, designers will want to use
the latest modeling programs and the fastest computers to rebuild
the catalog with high accuracy. By creating the tools to build a
catalog today, we can get a glimpse of the techniques and
pitfalls of designing mechanical structures in which 'every atom
is in its place.'

Reference

Ted Kaehler is a computer scientist who spent his sabbatical
from Apple Computer working with the Foresight Institute. He and
Foresight would like to thank Martin Saunders of Yale for
allowing us to use the program STRFIT3 and for his additional
help. Ted's participation was funded by the Restart Program of
Apple Computer, Inc.